Download Appendix S1 Relation of local short

Appendix S1
Relation of local short-term SPs and local EEG oscillatory states
The usage of local short-term SPs for characterisation of local EEG oscillatory states is
justified due to the following reasoning:
(i) A single EEG spectrum reflects the coordinated activity of tens and hundreds of
thousands of neurons at a particular point in time [1]. However, there is no simple (oneto-one) relation between a power spectrum computed from short epochs of ongoing EEG
and the actual state of the neurons in the underlying network: many different
configurations of firing neurons can give rise to a particular short-term SP (many-to-one
relation). At the same time, the same configuration of firing neurons cannot give rise to
two (or more) different short-term spectra. Thus, two different short-term power spectra
most likely are originated from two different configurations of firing neurons [2].
Consequently, short-term SP characterises/reflects a particular class of neurons’
activities, where each of the activities has something common with the others within the
class (one-class–to–one relation). Moreover, two classes of neurons’ activity do not
overlap (otherwise the same configuration of firing neurons could give rise to two or
more different short-term spectra). Thus, a given type of short-term SP may be
considered as a single event (which reflects a particular class of neurons’ activity) in
EEG phenomenology from viewpoint of its spectral characteristics [3]. In this context it
can be suggested that the SPs within each class are generated by similar neurodynamics
class as well as driving force [2]. SPs from different classes, however, are expected to
have different driving forces and therefore generated by different neurodynamics classes.
Thus, each perceptual, cognitive, or mental operation is thought to constitute a single
distinguishable neurophysiological state with a distinct and reliable SP type [4-7].
Therefore, the abrupt transition from one SP type to another reflects a change in the
transient neuronal assembly state or changes in the activity of the two or more neuronal
assemblies [8]. In this case, the frequency of appearance of each SP type reflects the
probability for the occurrence of particular neuronal dynamics class, which constitute a
dynamic repertoire of brain activity under a particular functional state or condition.
(ii) It is often claimed that volume conduction is the main obstacle in interpreting local EEG
data: each EEG electrode registers activity from many sources – in other words, locally
registered EEG activity is a result from a mixture of volume conduction effect and
genuine local source activity. However, it is often ignored that only some sources
contribute to local EEG considerably and others insignificantly. What is the contribution
of volume conduction effect in this context?
Firstly, volume conduction effect is distance dependent: the larger the distance of the
recording electrode from the current source, the less informative the measured potential
becomes about the events occurring at the location(s) of the source(s) [9]. Secondly,
superficial sources contribute a strong potential that is restricted in extent to nearby
electrodes on the scalp, and are thus the most likely sources to be accurately localized
with scalp recordings [10]. It has been estimated that one electrode integrates cortical
input under a scalp surface of the order of 6 cm2 [11-14]. Therefore, at distances greater
than 4 cm volume conduction effect is predicted to be very small [14].
Such prediction is supported by experimental findings which suggested the existence
of statistical heterogeneity (anisotropy) of electromagnetic field in regard to the
processes in local LFP [15] and local EEGs [16-20]. It was demonstrated that such
electromagnetic heterogeneity relates to large-scale morpho-functional organization of
the cortex:
(a) Covariance between neighboring electrodes across cortex functional boundaries
(e.g., parietal to temporal areas) is much smaller than covariance within functional
regions (e.g., left parietal to midline parietal area), indicating that multiple distinct
functional areas are assessed by topographic EEG [21; 22]. This morpho-functional
heterogeneity of EEG was also confirmed in independent study in which the spatial
heterogeneity of scalp-recorded EEG synchronicity was measured along longitudinal
(the anterior-to-posterior and posterior-to-anterior directions) and transversal (rightto-left anterior and right-to-left posterior directions) electrode arrays with scalp
electrodes equally spaced in all these arrays [17]. Data from actual EEG was
compared with so-called “surrogate” EEG in which a mixing of actual local EEG
recordings was done in such a way that each local recording was registered in a
different time so that the natural time relations between all local EEG recordings in
such EEG were completely destroyed, however, the number and the sequence of
segments within each local recording remained the same as in the actual EEG. For
longitudinal electrode arrays, despite the fact that all testing pairs of EEG electrodes
had the same interelectrode distance, synchronicity index exhibited the notable
topological landscape: it significantly decreased in locations of EEG electrode pairs
on the head which overlay cortex functional boundaries [17]. This data clearly
indicate that at the boundaries of well-outlined functional cortical areas the temporal
consistency of segmental architectonics of electrical field becomes weak.
Additionally (i) the relationship between synchronicity index and interelectrode
distance was not monotonous for both longitudinal electrode arrays: step-wise
dependency was observed and (ii) forward (posterior-to-anterior) and backward
(anterior-to-posterior) dependences of synchronicity index from the interelectrode
distance were significantly differing between each other [16, 17]. These results
suggest that volume conduction role here is insignificant. For transversal electrode
arrays it was demonstrated that (i) anterior and posterior cortex areas had opposite
tendencies in the dynamics of synchronicity index (notice that anterior and posterior
cortex areas have different morpho-functional organisation) and (ii) maximal
synchronicity index values in the posterior cortical areas were obtained for
homological lateral EEG locations (which have similar morpho-functional
organisation) in spite of the largest interelectrode distance in the electrode array [16,
17];
(b) The probabilities of firing of neurons observed singly and in small groups
simultaneously are in close statistical relationship to the EEG recorded in the near
vicinity [23, 24]. Therefore local EEG can provide an experimental basis for
estimating the local mean field of contributory neurons;
(c) The accuracy of topographic EEG mapping for determining local (immediately
under the recording electrode) brain activity was demonstrated [184, 185]: there are
statistically significant linear relationships between local EEG power and cerebral
perfusion underlying the electrode in the majority of frequency bands [25, 26].
These findings are in line with earlier study of Inouye et al. [27], where the authors
demonstrated that endogenous EEG activity originated from underlying cortex area
contributes the most to the spectral power measured from the given EEG electrode.
Whereas exogenous EEG activities originated from the other cortical areas
contribute to spectral power of the same EEG electrode insignificantly. Thus,
together described works suggest that topographic EEG mapping can accurately
reflect local brain function and that it is comparable to other topographic methods;
(d) Each local EEG or small group of local EEGs are characterised by a relatively
specific set of SP types [28] presumably due to their different degree of involvement
in the condition or the task;
(e) The same type of SP is usually observed simultaneously within the same
observation in two functionally homologous EEG channels: for example O1-O2
[29], thus suggesting functional topology of SP types rather than volume conduction
effect;
(f)
Cortex areas separated by distances exceeding the diameters of ‘wave packets’ have
differing wave forms and therefore different SP types [30, 31]. The coordinated
activity manifests a ‘wave packet’ that requires synchronization of a shared carrier
wave of the outputs of a large number of neurons over the area [30, 31];
(g) Topographically specific modulation of local EEG rhythms by direct cortical
stimulation via TMS in TMS–EEG studies have been demonstrated [32-35]. Such
TMS-induced entrainment of local brain oscillations due to direct interaction with
the underlying local generator revealed causal relations between local EEG
oscillations and underlying local generator;
(h) Compared to the EEG, the MEG is very little affected by the type and location of
tissue surrounding the generator, and especially that of tissue lying between the
generator and the sensor [36]. Additionally, the MEG is much more directly related
to the intracranial currents and is therefore less sensitive to the details of the skull
conductivity [37]. All these minimize volume conduction effect in MEG [38].
Analysis of local signals for EEG and MEG registered simultaneously revealed the
same classes of SP types and very similar percent ratio of these classes and very
similar temporary stabilization of SPs between EEG and MEG [39]. These results
suggest that volume conduction effect on SP analysis based on power spectra shape
is insignificant at least for 64-channel EEG.
There could be several reasons for these experimental results:
(a) as the spatial resolution of EEG has been estimated to be approximately 2 cm [40]
to 5 cm [14, 41] with an electrode spacing of approximately 7 cm as in the 10/20
System (used in the majority of EEG studies) volume conduction effect becomes
less likely;
(b) the spatial damping is very high, and thus global resonant modes play no significant
part in the generation of wave activity [42; 43];
(c) volume conduction does not spread all forms of activity [15];
(d) spread of activity in the cortex is not uniform in all directions as it follows from
measurements of tissue resistance [44], as well as from measurements of spread of
activity parallel and perpendicular to the surface by means of microelectrode arrays
[45, 46];
(e) volume conduction in tissues overlying the cortex is found to affect the spectrum
significantly only above about 25-30 Hz [47]. Note that most of the physiological
rhythms and approximately 98% of spectral power lies below that limit [48], and has
the highest signal-to-noise ratio;
(f) the conductivity values of the tissue compartments of the head (white-matter, graymatter, CSF, skull, and scalp) are not well-known, so that even an exact geometric
model of the head is still only an approximate volume conduction model of the head
[173]. Additionally, volume conduction models focus at physical and anatomical
constrains but do not take into consideration physiological data, e.g. the activity
(state) of cortex areas. However, macroscopic measurements in cortex revealed a
frequency dependence of electrical parameters (the conductivity and permittivity)
[49]. The extracellular medium is reactive in the sense that it reacts to the electric
field by polarization effects [50]. Electric polarization influences the frequencydependent electric properties of the tissue what allows the electrical parameters (the
conductivity and permittivity) to depend on frequency, as demonstrated by
macroscopic measurements [49, 51, 52]. Electric polarization is a prominent type of
reaction of the extracellular medium to the electric field. In particular, the ionic
charges accumulated over the surface of cells will migrate and polarize the cell
under the action of the electric field [50]. This surface polarization phenomena can
have important effects on the propagation of local field potentials [53]. Important,
the electrical field produced by neural activity can influence it back: studies have
found that (i) extremely weak fields (<0.5 mV/mm) are capable of significantly
modulating activity at the network and single cell level, (ii) endogenous fields are
involved in generating and maintaining neural oscillations and (iii) functional field
effect interactions in the brain are shaped by the temporal dynamics of neural
activity especially when relatively homogeneous populations of neurons are
synchronously active (for the review see [54], see also [55]).
Considering that all activities (influences) from multiple primary sources are not just
mixed, summed or averaged in a given cortex area, but are rather integrated within the
current state (activity) of the given area [56, 57], the local EEG registered from that area is
considered to represent a functional source, which is defined as the part or parts of the brain
that contribute to the activity recorded at a single sensor [58, 59]. A functional source is an
operational concept that does not have to coincide with a well-defined anatomical part of the
brain, and is neutral with respect to the problems of localization of primary source and
volume conduction [58, 59].
Considering the aforementioned findings one may suggest that local EEG short-term
SPs are mainly determined by underlying neurodynamic (functional state) and type of SPs
reflects mainly large-scale morpho-functional organization of the cortex rather than the effect
of volume conduction at least for 10/20 System (used in the majority of EEG studies) which
measures the main cortex lobes.
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